prof. dr. philippecattin: computed tomography …prof. dr. philippecattin: computed tomography...

ComputedTomography

Biomedical ImageAnalysis

Prof. Dr. Philippe Cattin

MIAC, University of Basel

April 11th/12h, 2016

April 11th/12h, 2016Biomedical Image Analysis

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Prof. Dr. Philippe Cattin: Computed Tomography

Contents

Abstract

1 Computed Tomography Basics

Introduction

Computed Tomography

Hounsfield's CT Prototype

EMI-Scanner

Detectors

Important Terminology

2 Single Slice CT

First Generation CT Scanner Design

Second Generation CT Scanner Design

Third Generation CT Scanner Design

Fourth Generation CT Scanner Design

Spiral Scanning CT

Spiral Scanning CT (2)


Drawback of these Designs

3 Multi-Detector Row CT

Multi-Detector Row CT

Detector Design

Detector Design (2)

Detector Design (3)

Detector Design (4)

Detector Design (5)

Detector Design (6)

Dual Source CT

Open Dual Source CT

Advantage of the DSCT

4 Image Reconstruction

4.1 Introduction April 11th/12h, 2016Biomedical Image Analysis

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Image Reconstruction

Image Reconstruction (2)

4.2 Radon Transform

Radon Transform

Parallel Projection

The Radon Transform

The Discrete Radon Transform

Radon Transform Examples

Radon Transform Examples (2)

4.3 Fourier Slice Theorem

Fourier Slice Theorem

Fourier Slice Theorem (2)

Reconstruction with the Fourier Slice Theorem

Reconstruction with the Fourier Slice Theorem(2)

4.4 Filtered Backprojection

Principle of Filtered Back-Projection

Numerical Back-Projection Example

Example Reconstructions

Example Reconstructions (2)

4.5 Helical Reconstruction

Helical Reconstruction

360° Linear Interpolation


4.6 Hounsfield Unit

Hounsfield Unit

5 Artefacts

Artefacts

Partial Volume Effect

High Density Artefacts

Gating in Cardio CT

CT and Medical Image Analysis


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(2)


Abstract

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ComputedTomography Basics


(4)Introduction

One of the major disadvantages associated with conventionalplanar radiography is its inability to produce sectional information.

The images produced on film represent the total attenuation of theX-ray beam as it passes through the patient. Depth information iscompletely lost!

Two general classes of tomography exist that solve this problem:

Linear tomography, which produces longitudinal sections

Computed axial tomography, which produces sectional or axial

slices

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Computed Tomography Basics

(5)


Computed Tomography

→ Computed Tomography (CT)[http://en.wikipedia.org

/wiki/Computed_axial_tomography] originallyknown as Computed Axial Tomography(CAT) or Body Section Röntgenographyis a medical imaging modality used togenerate 3D images of the internals ofan object from a large series of 2DX-ray images taken around a single axisof rotation.

→ Godfrey Newbold Hounsfield[http://en.wikipedia.org

/wiki/Godfrey_Newbold_Hounsfield] conceivedthe CT scanner idea in 1967 andpublicly announced it in 1972. → AllanMcLeod Cormack [http://en.wikipedia.org

/wiki/Allan_McLeod_Cormack] independentlyinvented a similar process and theyshared the Nobel price in 1979.

Fig 9.1: CT Apparatus

It is claimed that the CT scanner was the greatest legacy ofthe Beatles; the massive profits from their record salesenabled EMI to fund scientific research

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Hounsfield's CT Prototype

The original 1971 prototype took parallel readings through angles, each apart, with each scan taking a little over fiveminutes. The images from these scans took hours to beprocessed by algebraic reconstruction techniques on a largecomputer.

Fig 9.2: Hounsfield's original CT prototype Fig 9.3: Principle of theprototype

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EMI-Scanner

The EMI-Scanner was the firstproduction X-ray CT machine. It waslimited to scan two adjacent slices ofthe brain, but acquired the image datain about . The computation timewas about per picture.

The scanner required the use of awater-filled Perspex tank with apre-shaped rubber head-cap at thefront. The water-tank was used toreduce the dynamic range of theradiation reaching the detectors(scanning outside the head vs. throughthe skull).

The images were relatively lowresolution, being composed of a matrixof only .

The CT scanner was a huge success: by1977 1130 machines were installedacross the world.

Fig 9.4: EMI brain scanner witha Data General Nova

minicomputer. The first scannerwas installed at Atkinson

Morley's Hospital, Wimbledon,England in 1971

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Detectors

→ Scintillator [http://en.wikipedia.org/wiki/Scintillator] Detectors

Low maximum count rate leads to longer scan times or more imagenoise

Xenon Gas Detectors

Pressurised Xe gas capable of higher count rates, but low detectionefficiency

Modern Ceramic → Scintillators [http://en.wikipedia.org/wiki/Scintillator]

Coupled with photodiodes these detectors offer the bestperformance

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Important Terminology

In-plane resolution:

acquisition resolution in the

-plane

Out-of-plane, through-plane

resolution: slice distance in

axis

Anisotropic scan: the

resolution in the axis is

generally less than in the

axis

Isotropic scan: the voxel

dimensions are equal in the

, and axis

Fig 9.5: Coordinate system generallyused

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Single Slice CT


(11)First Generation CT ScannerDesign

The generation of CT scanner usedthe translate-rotate geometry.

The EMI scanner, for instance, used apencil X-ray beam and a singledetector. During translation of thegantry, the X-ray beam was sampled160 times. After a rotation of a newprofile was acquired. This procedurewas repeated for 180 different anglesand took roughly .

To minimise patient movement the headwas usually clamped.

Fig 9.6: First generation CTprinciple

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Single Slice CT

(12)


Second Generation CTScanner Design

The generation scanner tried toreduce the excessive scan times byusing a small fan beam with multipledetectors (up to 30 in some designs).

Scan times of between werepossible with this design.

The introduction of multiple detectorswas an important development.

Fig 9.7: Second generation CTprinciple

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Single Slice CT

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Third Generation CT ScannerDesign

The generation brought down scantimes even further by using the rotate-rotate geometry.

As the large fan beam encompasses thepatient completely the translatorymotion of the previous designs can beavoided. The X-ray tube and thedetector array rotate as one about thepatient.

The number of detector elements istypically in the hundreds.

To avoid excessive variations in signalstrength various manufacturers use abow-tie shaped filter to suit the body orhead shape.

Fig 9.8: Third generation CTprinciple

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Single Slice CT

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Fourth Generation CTScanner Design

The generation CT uses arotate-fixed ring geometry where thering of detectors completely surroundsthe patient.

As the X-ray tube must be closer to thepatient than the detectors it has a poorradiographic geometry, i.e. largegeometric magnification.

Scan times as low as withinterscan delays of can beachieved with this type of geometry.

Using many thousand detectorelements a in-plane resolution of

can be obtained.

Fig 9.9: Fourth generation CTprinciple

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Single Slice CT

(15)


Spiral Scanning CT

Advances in slip-ring technologyhave enabled the X-ray tube torotate continuously in the samedirection which overcomesproblems of interscan delays.

If the continuous motion of thegantry is combined with acontinuous advance of thepatient table along thelongitudinal axis we have aspiral/helical scanner.

The spiral scanning technologybrought about a significantreduction in scan times.

The gained speed came at aprice of increased complexity forreconstructing the helical data.

Fig 9.10: Illustration of helical scanning

Fig 9.11: Nice 3D rendering of helicalCT

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Single Slice CT

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The X-ray source iscollimated to a fan beamrotating around thepatient.

The X-ray tube and thedetectors are fixedtogether as a singlerotating unit.

Post patient collimationdefines the slicesensitivity profile.

Fig. 9.12: Basic design of a single slice CT usedin a spiral CT

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Single Slice CT

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In the context of helical scanning aparameter called Pitch is defined as the

Ratio of the distance that thepatient couch moves in onerotation to the collimationthickness (number of slices slice thickness)

(9.1)

In other words, for a couch advance of and a nominal collimation width

of , the pitch is 1. Pitch valuesare typically in the range of 1 to 2depending on the required spatialresolution in the direction of the couchmotion. Its a coverage indicator, inother words.

Fig 9.13: Pitch

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Single Slice CT

(18)


Drawback of these Designs

Ideally, volume data are of high isotropic spatial resolution, haveminimal motion artefacts, and optimally utilise the contrast agentbolus.

To reduce motion artefacts CT examinations need to be completedwithin a certain time frame, e.g. on breath hold, forthe heart.

If, however, a large scan range such as the entire thorax has to becovered

a thick collimation (large inter slice distance)

must be used, leading to anisotropic voxel sizes (whilst the in-planeresolution only depends on the system geometry).

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Multi-Detector RowCT


(20)Multi-Detector Row CT

Strategies to achieve a betterlongitudinal resolution andfaster scans include thesimultaneous acquisition ofmultiple slices at a time, thustermed Multi-Detector Row CTor Multi-Slice CT (MSCT).

Interestingly, the very firstcommercial CT systems(EMI-Scanner and SiemensSiretom) were already two-slicesystems. Only the introduction ofthe helical scanning principleallowed to fully leverage theadvantages of multi-detector rowCT.

Fig 9.14: Multi-slice CT

Fig 9.15: SOMATOM Sensation 16Gantry (Siemens)

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Detector Design

The figure shows, how different slice widths can be achieved byprepatient collimation for a single slice detector .

Fig 9.16: Prepatient collimation of the X-ray beam to obtain different slicethicknesses with a single detector row CT.

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Detector Design (2)

The principle can be easily extended to slices if the sensor isseparated midway along the axis.

Fig 9.17: Collimation of the X-ray beam to obtain different slice thicknesses with atwo detector row CT.

For detectors a more elaborate detector design is required.

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Detector Design (3)

The various manufacturers introduceddifferent detector designs in order toallow utmost flexibility in selecting slicewidths.

All designs combine several detectorrows electronically to a smaller numberof slices according to the selected slicewidth.

The total coverage of this detectordesign is (measured in theisocenter).

With prepatient collimation thefollowing slice widths can be realised:

, , , and .

Fig 9.18: Fixed array detector,16 rows, 4 slices

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Detector Design (4)

A more efficient approach (needs lessdetector channels) uses the adaptivearray design.

This design allows the followingcollimated slice widths: two slices at

, four at , four at ,two at , and two at .

Fig 9.19: Adaptive arraydetector, 8 rows, 4 slices

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Detector Design (5)

Sixteen-slice CT systems usually haveadaptive array detectors similar to theone depicted in Fig 9.20. It uses 24detector rows with a total coverage of

at the isocenter.

By properly combining the detectorrows, either 12 or 16 slices with

or can be acquiredsimultaneously.

Fig 9.20: Adaptive arraydetector, 24 rows, 16 slices

(Siemens)

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Detector Design (6)

32, 40, and 64 slice systems are now available.

Fig 9.21: Toshiba detector mock-ups

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Dual Source CT

A different approach to acquire moreslices in parallel was followed bySiemens with their → Dual SourceCT [http://www.siemens.com/dualsource]

(SOMATOM Definition).

Fig 9.22: Dual Source CT (SiemensSOMATOM Definition)

Fig 9.23: Comparison of LAD & Cxin diastole and systole

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Open Dual Source CT

Fig 9.24: Movie of the an open rotating dual source CT

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Advantage of the DSCT

The scan is in cardiac-mode virtually independent of the heart

rate → no -blocker needed

If the two X-Ray tubes are operated with two different tube

voltages (other spectra) tissue types can be better

differentiated

Fig 9.25: HU values for different tissue types (theoretical simulation)

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ImageReconstruction

Introduction


(32)Image Reconstruction

From the scanning process we have a set of image projections.Given these projections we want to determine the X-rayattenuation coefficients of the original image as accurate aspossible.

Fig 9.26: Image projections

Fig 9.27: A small section of the finalmatrix showing individual attenuation

values combined as a ray-sum

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Introduction

(33)


Image Reconstruction (2)

Already in 1917 → Johann Radon [http://en.wikipedia.org/wiki/Johann_Radon]

published a paper with the mathematical theory, the → Radontransform [http://en.wikipedia.org/wiki/Radon_transform], useful toreconstruct a 2D image from multiple projections such as in CTsystems.

Hounsfield used, for the first CT scanner, an iterative technique toexactly solve the Radon transform. Its disadvantages are that it isslow and that all data must be collected before reconstruction canbegin.

Todays CT systems mainly use variants of the filteredback-projection approach that is computationally more efficient.

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Radon Transform


(35)Radon Transform

A straight line in Cartesiancoordinates can be either describedby its slope-intercept form

(9.2)

or by its normal representation

(9.3)

see Fig 9.28.

Fig. 9.28: Different linerepresentations

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Radon Transform

(36)


Parallel Projection

An arbitrary point in the projection is given by the raysum alongthe line

(9.4)

in the continuous space the raysum is then given by

(9.5)

where is the impulse

function.

(9.6)

with .

The integrand is zerounless the argument inthe delta function is

zero. This is valid for allpoints on the line

.

Fig. 9.29: Projection geometry

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Radon Transform

(37)


The Radon Transform

We can generalise this equation to arbitrary lines

(9.7)

This projection is called Radon transform. Often used notations forthe Radon transform of are

(9.8)

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Radon Transform

(38)


The Discrete RadonTransform

In the discrete case the integrals in the Radon transform arereplaced by sums

(9.9)

The Radon transform forms the corner stone ofreconstruction from projections used e.g. in ComputedTomography, PET, SPECT.

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Radon Transform

(39)


Radon Transform Examples

The figure below shows an example image with its Radontransform. The interpretation of the sinogram is still quite easy.

Fig. 9.30: Double box image

Fig. 9.31: Sinogram of the double boximage with projections over

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Radon Transform

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Radon Transform Examples(2)

The figure below shows an example phantom with its Radontransform. The interpretation of the sinogram is not possibleanymore, although the phantom's structure is quite simple.

Fig. 9.32: Shepp-Logan phantom

Fig. 9.33: Sinogram of the phantomwith projections over

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Fourier SliceTheorem


(42)Fourier Slice Theorem

In the following slide we will relate the Fourier transform of 1-Dprojection with the 2-D Fourier transform of the scanned object.Without loss of generality, we take the projection line to be the -axis in the derivation below. Given is the image and its

projection onto the -axis where

(9.10)

The Fourier transform of is

(9.11)

the slice at is then

(9.12)

which is the Fourier transform of .

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(43)


Fourier Slice Theorem (2)

Fig. 9.34: Graphical representation of the Fourier slice theorem

The Fourier slice theorem states that, the 1-dimensionalFourier transform of a projection corresponds to the slice(line) - at the same angle - in the 2-dimensional Fouriertransform of the object

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Reconstruction with theFourier Slice Theorem

In principle we could reconstruct the image by filling up the

Fourier space with the Fourier transforms of the individual

projections and then calculate the inverse Fourier transform. Thisapproach is, however, computationally very expensive.

Fig. 9.35: Image reconstructing using the Fourier slice theorem

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Reconstruction with theFourier Slice Theorem (2)

If we just sum the spectra ofthe individual projectionbeams, the spectral densityfor low frequencies would betoo high as the beams arecloser to each other for smallradii → lower frequencies toostrong.

We therefore must correctthe spectrum with a suitableweighting factor. As thedensity of the projectionbeam goes with

(Frequency) the spectra mustbe multiplied with → ramp

filter.

Each projection directionthus has to be multiplied witha suitable weighting function

. As will be seen in the

next section, this can also beperformed as a convolutionwith the inverse Fouriertransform of in the

spatial domain → filteredback-projection.

Fig. 9.36: Spectral density must becorrected to get suitable results

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FilteredBackprojection


(47)Principle of FilteredBack-Projection

(1) The measured projections are smeared back, i.e. combined as aray-sum, across the output matrix. (2) As the back-projected imageis heavily blurred and shows star artefacts it has to be filtered witha highpass yielding the final reconstructed image.

Fig 9.37: Filtered back-projection principle

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Filtered Backprojection

(48)


Numerical Back-ProjectionExample

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Example Reconstructions

Back-projectionwithout filteringusing 2, 4, 8,16, and 32projections.

Strong artefactscan be seen andthe images areheavily blurred.

Fig 9.38: Back-projection without filter

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Example Reconstructions (2)

Back-projectionwith highpassfiltering usingthe same 2, 4, 8,16, and 32projections.

Strong artefactscan be seen andthe images areheavily blurred.

Fig 9.39: Back-projection with filter

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HelicalReconstruction


(52)Helical Reconstruction

We would like to use the same filtered back-projection method asbefore:

Choose the

interpolation

position along

the z-axis

Only one

projection is

from the

reconstruction

position, others

are from

different

z-positions

Fig 9.40: Problem of the helical reconstruction

→ Introduces artefacts when the structures change along thez-axis.

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Idea: Use attenuation data from points apart on the helix forinterpolation

Fig 9.41: Interpolation

→ Interpolation makes the effective image width broader.

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Idea: Use attenuation data from complementary projections inaddition to points apart on the helix

Fig 9.42:Complementary

projections

Fig 9.43: Interpolation

→ Slice profile is narrower, as the z-axis distances are shorter thanin interpolation.

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Hounsfield Unit


(56)Hounsfield Unit

The tissue absorption coefficient depends on the tube voltage.

To make them comparable, theabsorption coefficients have tobe related to that of water a thesame tube voltage. This way anumber [Hounsfield unit = Hu]insensitive to tube voltage canbe obtained:

(9.13)

In practice CT values areproduced from for air,

for water, and between for bone.

Fig 9.44: Common CT numbers

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Artefacts


(58)Artefacts

Several inherent CT artefacts have an important influence on theapplied Medical Image Analysis Methods and generally need to beaccounted for:


High density artefacts

Gating in Cardio CT

The Good News: CT data is geometrically very accurate. IfMR/US data is to be registered with CT, then CT should beused as the reference!

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Artefacts

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The partial volume effect,common to most medicalimaging modalities, poses animportant problem for manymedical image analysis methods.

The sampling of the imagingvolume renders itdifficult/impossible to exactlylocate the boundary of an object.

If not taken special care of, asimple shift of the object candrastically change the result,e.g. area measurement in Fig9.45(c)+(d). The measured areaof (d) is higher than thearea of (c).

Fig 9.45: (a) Original object, (b) objectsampled on a discrete grid, (c)

thresholded object, (d) thresholdedshifted object

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Artefacts

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High Density Artefacts

High density streak artefacts or Windmill artefacts result from thefinite width of the detector rows, which require interpolation. Theartefacts appear close to high contrast gradients.

Fig 9.46: High density artefact example

Fig 9.47: Windmill effect

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Artefacts

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Gating in Cardio CT

For many acquisitions of the heart and arterial system ECG gatingis used. To reduce exposure, the AEC reduces the tube current to

during systole (when no images are captured). Proper gating,however, depends on a regular sine rhythm not present in alldiseased patients.

Fig 9.48: Image of good quality withdecent SNR

Fig 9.49: Gating failed, image wasacquired with of the dose → very

noisy image

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Artefacts

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CT and Medical ImageAnalysis

Medical image analysis is an indispensable tool in CT. Without theaid of advanced image analysis methods, radiologists would needsubstantially more time to find interesting location in the CTdatasets.

Fig 9.50: Plaque detection aid

Fig 9.51: Automatic dissectionsegmentation

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prof. dr. philippecattin: computed tomography …prof. dr. philippecattin: computed tomography...

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